Final answer:
All children of two heterozygous deaf parents with an autosomal dominant gene could potentially have normal hearing if they inherit the homozygous recessive genotype (dd). However, the probability of all children having normal hearing is less likely with each additional child.
Step-by-step explanation:
In a mating involving a deaf man and a deaf woman where both have a rare autosomal dominant gene causing deafness, it is possible for all their children to have normal hearing if both parents are heterozygous for the gene (Dd), meaning they each carry one deafness allele (D) and one normal allele (d). If both parents are heterozygous, the offspring could have the following genotype combinations: DD, Dd, dD, or dd. The only combination where the child would have normal hearing is the homozygous recessive (dd). Since each child has an independent chance of inheriting the alleles, it is theoretically possible for all children to be dd and therefore have normal hearing, although the likelihood decreases with the number of children.
An individual with an autosomal dominant disorder will express the disease even with one copy of the allele. In contrast, autosomal recessive disorders require an individual to have two copies of the recessive allele to express the disease, and carriers will not display symptoms. When considering the possibility of offspring with normal hearing from two deaf parents with an autosomal dominant gene, it's critical to analyze the parents' genotypes, not the rarity of the gene.